Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
M/M/1 queues with working vacations (M/M/1/WV)
Performance Evaluation
The Discrete-Time GI/Geo/1 Queue with Multiple Vacations
Queueing Systems: Theory and Applications
M/G/1 queue with multiple working vacations
Performance Evaluation
Vacation Queueing Models: Theory and Applications (International Series in Operations Research & Management Science)
Discrete-time GI/Geo/1 queue with multiple working vacations
Queueing Systems: Theory and Applications
Analysis of the M/G/1 queue with exponentially working vacations--a matrix analytic approach
Queueing Systems: Theory and Applications
The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation
Performance Evaluation
Performance analysis of M/G/1 queue with working vacations and vacation interruption
Journal of Computational and Applied Mathematics
Analysis of a GI/M/1 queue with multiple working vacations
Operations Research Letters
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Consider a GI/Geo/1 queue with multiple vacation policies described as follows: when the system becomes empty, the server either begins an ordinary vacation with probability q(0@?q@?1) or takes a working vacation with probability 1-q. During a working vacation period, customers can be served at a lower rate. If there are customers in the system at a service completion instant, the vacation can be interrupted and the server will come back to the normal busy period with probability p(0@?p@?1) or continue the working vacation with probability 1-p. Using the matrix-analytic method, we obtain the steady-state distributions for the queue length both at arrival and arbitrary epochs. The sojourn time is also derived. Finally, we present some numerical examples and use the parabolic method to search the optimum value of service rate in working vacation period.